Effect of Structure on the Electronic Density of States of Doped Lanthanum Cuprate

ofDopedLanthanumCuprate

M.R.NormanMaterialsScienceDivision

arXiv:cond-mat/9306011v1 3 Jun 1993ArgonneNationalLaboratory

Argonne,IL60439G.J.McMullanCavendishLaboratoryMadingleyRoadCambridgeCB3OHE,UKD.L.NovikovandA.J.Freeman

ScienceandTechnologyCenterforSuperconductivityand

DepartmentofPhysicsandAstronomy

NorthwesternUniversityEvanston,IL60208

Wepresentaseriesofdetailedbandcalculationsonthevariousstructuralphasesofdopedlanthanumcuprate:HTT,LTO,andLTT.TheLTOdistortionisshowntohavelittleeffectontheelectronicdensityofstates(DOS).Afittothepressuredependenceofthesuperconductingtransitiontemperatureindicatesthatonly2.5%oftheDOSisaffectedbytheHTT→LTOtransition.TheLTTdistortionalsohaslittleeffectontheDOSfortheexperimentalvalueoftheoctahedraltiltangle.Largertiltangles,though,leadtoadramaticchangeintheDOS.

PACSnumbers:71.25.Pi,74.70.Vy

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Dopedlanthanumcuprate,La2−xMxCuO4,whereMistypicallySrorBa,istheprototypesystemfortheclassofcopperoxidematerialsknownashightemperaturesuper-conductors.Itexhibitsanumberofstructuralphases,eachofwhichhasdifferentsupercon-ductingproperties.TheHTT(hightemperaturebody-centeredtetragonal)phaseoccursforlowtemperaturesonlyforx>0.2,wheresuperconductivityissuppressed.Atlowertemperaturesforx<0.2,onefindstheLTO(lowtemperatureface-centeredorthorhombic)phase,whichissuperconductingoverarangeofxvalues.Nearx=0.125,theLTT(lowtemperatureprimitivetetragonal)phaseformsfortheBasystemwithsuppressedsuper-conductivity.AsmalldipinTcnearx=0.115isfoundintheSrsystem,butnoevidencefortheLTTphase.Moreinformationhasnowbeengatheredbyhydrostaticpressureexperiments1.FortherangeofxvalueswhereonehasasuperconductingLTOphase,theHTTphasecanbestabilizedbypressureandisactuallyfoundtohavemaximalTc.Nearx=0.125fortheBasystem,pressuredestroystheLTTphase,yetsuperconductivityisstillstronglysuppressed.

Understandingthisseriesofpuzzlingresultsmayhelptounravelthemysterybehindhightemperaturesuperconductivity.Anobviousfirststepinthisdirectionistounderstandtheeffectthesevariousstructuraldistortionshaveontheelectronicstructure.Ofcourse,manybandstructurecalculationshavebeenperformedonthesesystemsinthepast2.ArecentcalculationbyPickettetal3fortheLTTphaserevealedastrongsuppressioninthedensityofstates(DOS)neartheFermienergy(EF),whichtheythenconnectedtothesuppressedsuperconductivityofthisphase.Becauseofthisintriguingresult,andthevariousadditionalexperimentalphenomenamentionedabove,wedecidedtoperformaseriesofbandcalculationsforthevariousphases,accuratelycalculatetheDOSinthevicinityofEF,andattempttoconnecttheseresultstotheexperimentalobservations.

Weusethelinearizedmuffintinorbitalmethod4,includingcombinedcorrectionterms.Threeindependentcodeswereemployedaschecks,oneofwhichcontainsnon-spherical

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correctionstothepotentialinsidethemuffintins5(allthreecodesgavecomparableresults).Thecalculationspresentedinthispaperarescalarrelativistic,employtheHedin-Lundqvistformfortheexchange-correlationpotential,andusetwoemptyspheresperformulaunit(locatedatthe(1/2,0,1/4)pointsinHTTnotation).DopingwassimulatedbyreducingtheZvalueoftheLasite.Calculationswereconvergedona90kpointmeshinsidetheirreduciblewedgeoftheBrillouinzone.Forthefinaliteration,eigenvaluesfor180kpointsfortheHTTandLTOand144kpointsfortheLTTphaseweregeneratedandtheresultswerefitusingaFourierseriessplineanalysis.Thesplinefitwascheckedbyplottingbandsalongvarioussymmetrydirections,andthenusedtogenerateaDOSbasedonatetrahedraldecompositionofthezone(around1.6milliontetrahedrawereused).

TheHTTcalculationwasdoneusingthelatticeparametersofCoxetal6forx=0.1Baat295K.FourLTOcalculationswerecarriedout,onewhichusedtheresults6forx=0.1Baat91K,andthreewhichusednewresultsontheSrsystemat10Kforxvaluesof0.1,0.15,and0.27.TwoLTTcalculationswereperformed,onewhichusedtheresults6forx=0.1Baat15K,andanotherbasedonthetheoreticalparametersofPickettetal3obtainedbyminimizationofthetotalenergy8.Thelattersetofparametershasatiltangleofthecopperoxideoctahedraabouttwicethatoftheformer.

BeforemovingtothemaindiscussionontheDOS,wefirstcommentonthematterofrigidbandbehavior.ThishasbeenquestionedbasedonthefactthattheCuionwouldprefertobeclosetoad9configuration,andthusrigidbandbehaviormaynotbeobservedsincethestatesatEFareamixtureofCudandOpstates.Ourowndopingresults,basedonadjustingtheZvalueoftheLanucleus,exhibitanintriguingbehavior.WhileweindeedfoundrigidbandbehaviorintheDOS,thechargedensitydidnotexhibitsuchbehavior.Inparticular,theDOShasabout60%Cudcharacter,withtheremaindermostlyOp.Butcomparingchargesat0%dopingand10%doping,onlyabout20%ofthechangeinchargecamefromtheCudorbitals,withtheremaining80%comingfromtheLasite.We

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shouldnotethatthechargeontheLasiteisalmostallduetoreanalysisofchargefromthesurroundingOsitessincetheLMTOmethodusesoverlappingspheres.OurspeculationisthatthechangeinpotentialontheLasiteduetothereductionoftheZvaluecausesthechargeanalysisonthatsitetochangeinordertocompenstateforthechargelossduetodoping,thuslargelypreservingthedcountontheCusite.Thisoccurs,however,insuchawaythatrigidbandbehaviorismaintainedintheDOS.

InFig.1,weshowplotsoftheLTOandHTTDOSforthex=0.1Bacalculation.TheHTTresultsweregeneratedassumingLTOsymmetrysoastoeliminatedifferencesduetousingdifferentBrillouinzones.Asonecansee,therearevirtuallynodifferencesinthecurves.ThishasbeenfurtherverifiedbyplotsoftheFermisurfacewhichshownodetectabledifferencesbetweenHTTandLTO(the”gaps”seenintheLTOFermisurfaceplotsintheliterature2aresimplyazone-foldbackeffectandhavenothingtodowiththeorthorhombicdistortion).

WeshowplotsoftheLTODOSforthex=0.1,x=0.15,andx=0.2SrcalculationsinFig.2.Again,therearevirtuallynodifferencesinthecurves,indicatingagainthattheorthorhombicdistortionhasonlyaweakeffectontheDOS(wenotethattheorthorhombicdistortionincreasesasxdecreases).

PlotsoftheLTTandHTTDOSforthex=0.1BacalculationarepresentedinFig.3.TheHTTresultsweregeneratedassumingLTTsymmetrysoastoeliminatedifferencesduetothedifferingBrillouinzones.Thezeroofenergywassetat12.5%doping,wheretheLTTphaseisseenexperimentally.Again,therearevirtuallynodifferencesintheDOS.ThisindicatesthatthesuppressionofTcfortheLTTphaseisprobablynotconnectedwithadensityofstateseffect.

InFig.4,weshowplotsofourLTTcalculationforx=0.1BaversusacalculationdoneusingthelatticeparametersofthepreviousworkofPickettetal3.Wenotethat

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theoctahedraltiltangleusedintheirworkisaboutafactoroftwolargerthanwhatweusedbasedontheCoxetalparameters6.OnecanseethatthevanHovepeakissplitwiththePickettetal3parameters(ourDOSplotisverysimilartotheirs).ThevanHovepeakisalsosplitwithourchoiceofparameters,buttheeffectistoosmalltobenoticeableintheDOS.ThisdifferenceoccursbecausethesplittingofthevanHovepeakdependsquadraticallyonthetiltangle8.ThelargesplittinginthePickettetal3casegivesanotchintheDOSclosetoEFwhichledthemtosuspectthatthismightberesponsibleforthesuppressedsuperconductivity.Becauseofthisstrongdependenceontiltangle,itisofsomeimportanceforexperimentaliststoattempttoaccuratelydeterminetheoctahedraltiltanglefortheLTTstructure.

WeconcludethispartbyremarkingthattheLTOandLTTstructuraldistortionshavelittleeffectontheDOS,thoughlargedifferencesarefoundfortheLTTcasewithincreasedoctahedraltiltangle.Moreover,improvedsamplingofthezonebyusingmorecalculatedkpointsactstosharpenthecalculatedvanHovesingularity(thus,mostpublishedplotsoftheDOSunderestimatestheheightofthispeak).WeshouldalsoremarkthattheLMTOcalculationsplacethevanHovesingularityatabout21-22%doping,whereasFLAPWcalculationsplacethispeakatabout17%doping2.WehavefoundthatLMTOcalculationswhichdonotincludethecombinedcorrectiontermsplacethevanHovepeakatthesamedopingastheFLAPWcalculations,indicatingthatthelocationofthepeakissensitivetodetailsoftheelectronicstructurecalculation.

Wenowattempttoconnectsomeoftheseobservationswithexperiment.WestartwiththeLTO→HTTtransitioninducedbypressure1.Tcincreaseslinearlywithpressure,thensaturatesatthistransition.Thepressuredependenceofthestructuraltransitioncanbeestimatedfromanomaliesinthethermalexpansion.Todescribethis,weemployatheoryduetoBilbroandMcMillan9.Thistheoryassumesthatthesuperconductingpairpotentialisindependentofpressure,andthatthepressuredependencecomesfroma

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competitionbetweenaDOSchangecausedbythestructuraldistortionandtheformationofasuperconductinggap.Thisinvolvessolvingtwocoupledmeanfieldequationsinvolvingthesuperconductinggapandthechargedensitywavegap(assumedtoonlyoccuroverpartoftheFermisurface).Atapressurewherethetwotransitionsmerge,theratioofdTs/dptodTc/dp(whereTsisthestructuraltransitiontemperature,Tcthesuperconductingtransitiontemperature,andpthepressure)isequalto−(N−N1)/N1(whereNisthetotalDOS,andN1isthatpartoftheDOSremovedbythestructuraldistortion).Thedataforbothx=0.17andx=0.19(wheresomeinformationexistsforestimatingthepressuredependenceofthestructuraltransition)givevaluesofdTc/dp≃-5.75K/kbaranddTc/dp≃0.15K/kbar.Thus,N1/N≃0.025,i.e.,only2.5%oftheN(EF)valueisaffectedbythestructuraltransition.Suchasmallnumberiswithintheerrorbarsofthebandcalculations,andthusthedataindependentlysupportourconclusionthattheLTOdistortionhasaveryweakeffectontheDOS.Moreover,thistheorywouldalsopredictthatforpressureswherethestructuraltransitionisnear(butlargerthan)Tc,oneshouldseeasaturationoftheorthorhombicdistortionforTAsfortheLTO→LTTphasetransitionandtheresultantsuppressionofsuperconduc-tivity,ourconclusionbasedonthisworkisthatthedensityofstatesdoesnotplayanimportantrole.Thisisconsistentwiththepressuredata,whichshowthatevenwhentheLTTtransitionisgone,superconductivityisstillsuppressed.Recentdata10indicatethatmagneticorderingoccursforthisconcentrationrange,andthusisthemostlikelyreasonfortheTcsuppression.Giventhatbandstructurecalculationsdonotgiverisetoamag-netictransitionforstochiomentricLa2CuO4,wedonotexpecttobeabletodescribethismagnetism.Ashasbeennoted,themagnetismmaybeduetoacommensurationeffectatx=1/8.Moretheoreticalworkiscertainlyneededtoaddressthisinterestingeffect.

Inconclusion,wefindlittleeffectofthestructuraldistortionsofdopedLa2CuO4on

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theelectronicdensityofstates.ThisresultissupportedbysomeexperimentaldataonboththeHTT→LTOandLTO→LTTtransitions.

ThisworkwassupportedbytheNationalScienceFoundation(DMR91-20000)throughtheScienceandTechnologyCenterforSuperconductivity.MRNwasalsosupportedbytheU.S.DepartmentofEnergy,OfficeofBasicEnergySciences,underContractNo.W-31-109-ENG-38.MRNwouldliketoacknowledgethehospitalityoftheCavendishLaboratory,CambridgeUniversity,wheresomeofthisworkwasperformed(withaddtionalsupportfromtheUKSERCandTrinityCollege,Cambridge).WethankJimJorgensenandBerndSchuttlerforcallingourattentiontothisproblemandsuggestingthesecalculations.WealsoacknowledgehelpfulconversationswithDaleKoelling,andwithMikeCrawfordandDavidHinksconcerningtheexperimentaldata.WearealsoindebtedtoWarrenPickettandRonCohenformanycorrespondencesconcerningtheLTTresults.

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REFERENCES

1.N.YamadaandM.Ido,PhysicaC203,240(1992).2.W.E.Pickett,Rev.Mod.Phys.61,433(1989).

3.W.E.Pickett,R.E.Cohen,andH.Krakauer,Phys.Rev.Lett.67,228(1991).4.O.K.Andersen,Phys.Rev.B12,3060(1975).

5.M.Methfessel,C.O.Rodriguez,andO.K.Andersen,Phys.Rev.B40,2009(1989).6.D.E.Cox,P.Zolliker,J.D.Axe,A.H.Moudden,A.R.Moodenbaugh,andY.Xu,Mat.Res.Soc.Symp.Proc.156,141(1989).7.DavidHinks,privatecommunication.

8.TheauthorsthankWarrenPickettandRonCohenfortheirlatticeparametersandtheobservationaboutthequadraticdependenceofthevanHovesplittingontiltangle.

9.G.BilbroandW.L.McMillan,Phys.Rev.B14,1887(1976).

10.I.Watanabe,K.Kawano,K.Kumagi,K.Nishiyama,andK.Nagamine,J.Phys.Soc.

Japan61,3058(1992).

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FIGURECAPTIONS

1.Densityofstates(performulaunit)fortheHTTandLTOx=0.1Bacases.Thezeroofenergyisatx=0.1

2.Densityofstates(performulaunit)fortheLTOx=0.1,0.15,and0.2Srcases.Thezeroofenergyisatx=0.1

3.Densityofstates(performulaunit)fortheHTTandLTTx=0.1Bacases.Thezeroofenergyisatx=0.125

4.Densityofstates(performulaunit)fortheLTTx=0.1Bacase(Cox)andtheLTTcasewiththePickettetallatticeparmaters(Pic).Thezeroofenergyisatx=0.125